Adsorption potentials thermodynamics

The models presented above have also been reviewed in Ref 18. Recently, an expression for the adsorption potential at the free water surface based on a combination of the electrostatic theory of dielectrics and classical thermodynamics has also been proposed." ... 

The thermodynamic functions of fc-mers adsorbed in a simple model of quasi-one-dimensional nanotubes s adsorption potential are exactly evaluated. The adsorption sites are assumed to lie in a regular one-dimensional space, and calculations are carried out in the lattice-gas approximation. The coverage and temperature dependance of the free energy, chemical potential and entropy are given. The collective relaxation of density fluctuations is addressed the dependence of chemical diffusion coefficient on coverage and adsorbate size is calculated rigorously and related to features of the configurational entropy. 

Semiernpirical Isotherm Models. Some of these models have been shown to have some thermodynamic inconsistencies and should be used with due care. They include models based on the Polanyi adsorption potential (Dubinin-Radushkevich, Dubinin-Astakhov, Radke-Prausnitz, Toth, UNI LAN. and BET). 

There are cases, however, including the very common one of an air-water surface, where no ions can possibly pass the boundary thermodynamical equilibrium cannot therefore be set up between the water and air, and adsorption potentials (the surface potentials of Chapters II and III) are permanent. The usual method for measuring surface potentials with a radioactive air-electrode does not appreciably disturb the adsorption potentials the gaseous ions are very few and are attracted into the water by image forces so that no double layer, compensating the double layer in the water due to the dipoles of the molecules in the surface film, can build up in the air. 

Adsorption Potentials, Adsorbent Self-Potentials, and Thermodynamic Equilibria... 

Since the capillary condensate in a particular mesopore is in thermodynamic equilibrium with the vapour, its chemical potential, p°, must be equal to that of the gas (under the given conditions of T and p). As we have seen, the difference between p° and p1 (the chemical potential of the free liquid) is normally assumed to be entirely due to the Laplace pressure drop, Ap, across the meniscus. However, in the vicinity of the pore wall a contribution from the adsorption potential, 0(z), should be taken into account. Thus, if the chemical potential is to be maintained constant throughout the adsorbed phase, the capillary condensation contribution must be reduced. 

Jaroniec et al. [15] also proposed a simple thermodynamic approach to characterize microporous solids (JGC model). The MPSD, J(x), is related to the adsorption potential distribution through the following equation ... 

The electrical potential at an oil -j- water interface has been the subject of many investigations aimed at discovering the part it plays in bio-electric phenomena. These investigations tried to relate the changes of this potential to the nature of the ions in the aqueous solution. The observed results have been attributed to adsorption potentials, diffusion potentials 2 and thermodynamic phase-boundary potentials.3 It has been shown that the first of these suggestions is definitely false 4 and it seems likely that diffusion potentials and phase-boundary potentials have both made a contribution in the systems investigated hitherto. The attempts at quantitative correlation 2 can hardly be considered successful. 

The X(A) function is a primary thermodynamic characteristics of a given adsorption system and can be easily calculated by differentiating the equilibrium adsorption isotherm with respect to the adsorption potential A = RT In (po/p). Equation (2) shows that a simple... 

The two-dimensional gas model assumes no mutual interaction of the adsorbed molecules. It is believed that the adsorbent creates a constant (across the surface) adsorption potential. Thus, in the framework of statistical thermodynamics, the model describes adsorption as the transition of a gas with three translational degrees of freedom into an adsorbed state with one vibrational and two translational degrees. Assuming ideal behavior and using molar quantities, one obtains the standard entropy in the adsorbed phase as the sum of the translational and vibrational entropies from Eqs. 5.28 and 5.29 ... 

The relation of the various heats of adsorption to the adsorptive potential is shown schematically in Fig. 7.2. It should be noted that while heat lost from a system is thermodynamically a negative quantity, it is a custom of long-standing to employ a positive sign in adsorption science. This is frequently confusing to newcomers to adsorption studies. 

Davydov et al. [46] used IGC to determine several adsorption thermodynamic properties (equilibrium constants and adsorption heats) for the adsorption of organic compounds on C q crystals, and compared them with those obtained for graphitized carbon black. The adsorption potential of the surface of fiillerene crystals was much lower than that of a carbon black surface. The dispersive interaction of organic molecules with C q is much weaker than with carbon black. The adsorption equilibrium constant for alkanes and aromatic compounds is therefore lower in the case of fullerenes. Aliphatic and aromatic alcohols as well as electron-donor compounds such as ketones, nitriles and amines were adsorbed more efficiently on the surface of fiillerene crystals. This was taken as proof that fiillerene molecules have electron-donor and electron-acceptor properties, which is in agreement with the results of Abraham et al. [44]... 

Relative free energies determine important chemical quantities such as relative affinities of binding of ligands to receptor molecules, relative solubilities, relative electrode potentials of different substances, adsorption coefficients, and chemical potentials. Thermodynamic cycle free energy methodologies have become one of the most popular tools in the computational study of complex chemical systems. 

C. Thermodynamic meaning of the adsorptive potential Theoretical Background... 

These statements are valid in spite of the fact that in Eq. (3), the limiting value of the adsorption potential A tends to negative infinity as the equilibrium pressure tends to zero. Although this is thermodynamically inconsistent, the relation RT ln(P/Po) does hold true to a certain limit of low pressure. There is a lower bound on the interaction energy provided by a... 

At least two problems have to be solved before a consistent system of theories for supercritical adsorption becomes sophisticated first, how to set up a thermodynamically standard state for the supercritical adsorbed phase, so that the adsorption potential for supercritical adsorption can be evaluated Second, how to determine the total amount in the adsorbed phase (i.e., the so-called... 

E. Potential Theory of Adsorption and Thermodynamics of Surface Excesses... 

Here Ho n) is the thertnodynamical Hamiltonian of the adsorbate, j is the the adsorption potential of the j-th cell, uj2jk is the energy of the p>air interaction between the j th and k-th particles, is the chemical potential of the adsorbate, and Zp is the adsorbate partition function. Introducing the thermodynamical expression for adatom energy in adsorption cell... 

The Potential Theory as originally conceived by Polanyi is well documented in the classic text by Brunauer (1943). Polanyi considered contours of equipotential energy above solid surfaces and ascribed a volume to the space between the ith equipotential surface of energy e and the adsorbent surface. The potential was assumed to be independent of temperature so that = /(0) is essentially an isotherm equation. The adsorption potential is defined as the work of compression of the gas from a pressure p to the saturation pressure ps. For one mole of a perfect gas of volume v in an open thermodynamic system the adsorption potential is therefore... 

Stem layer adsorption was involved in the discussion of the effect of ions on f potentials (Section V-6), electrocapillary behavior (Section V-7), and electrode potentials (Section V-8) and enters into the effect of electrolytes on charged monolayers (Section XV-6). More speciflcally, this type of behavior occurs in the adsorption of electrolytes by ionic crystals. A large amount of wotk of this type has been done, partly because of the importance of such effects on the purity of precipitates of analytical interest and partly because of the role of such adsorption in coagulation and other colloid chemical processes. Early studies include those by Weiser [157], by Paneth, Hahn, and Fajans [158], and by Kolthoff and co-workers [159], A recent calorimetric study of proton adsorption by Lyklema and co-workers [160] supports a new thermodynamic analysis of double-layer formation. A recent example of this is found in a study... 

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